Katkova, Olga M.; Vishnyakova, Anna M. A continual analogue of a theorem by M. Fekete and G. Pólya. (English) Zbl 0972.44001 Positivity 5, No. 1, 1-11 (2001). Let \(p\) be continuous in \([a,b]\) with \(p(a)> 0\), \(p(b)> 0\), and \(L(x,p)= \int^b_a e^{xt}p(t) dt> 0\) for all real \(x\). The authors prove that for suitable small \(\varepsilon\) and for suitable large \(\lambda\) the product \(\exp(\lambda e^{\varepsilon x})L(x,p)\) is the Laplace transform of a nonnegative function. Also, a more complicated version is treated in the case that \(a=0\) and \(b= \infty\). Reviewer: Lothar Berg (Rostock) MSC: 44A10 Laplace transform 42A85 Convolution, factorization for one variable harmonic analysis 44A35 Convolution as an integral transform 60E05 Probability distributions: general theory Keywords:Laplace transform; nonnegative function PDFBibTeX XMLCite \textit{O. M. Katkova} and \textit{A. M. Vishnyakova}, Positivity 5, No. 1, 1--11 (2001; Zbl 0972.44001) Full Text: DOI